#5487 ⟨a, b | aaaaba=baaba⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 11
Infinite non-commutative monoid

Rewriting system

Format:	Pretty Plain
Word to reduce:
	Tips: Lowercase letters stand for generators. Spaces are ignored. Numbers repeat the previous letter, e.g. `b90`.
Reduction strategy:	Leftmost Rightmost
Path to normal form:	1 1

Reduction order:
- Right-to-left recursive path with deg(a) = deg(c) = 0, a < c; deg(b) = 1
Auxiliary generators:
1. baaba=c
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	a⁴cac ⇒ ca⁵c	[12]
2.	a⁸c ⇒ cac	[10]
3.	a⁴ca⁵c ⇒ c(ac)²	[13]
4.	caba ⇒ a⁴c	[6]
5.	a⁴ba ⇒ c	[2]
6.	cabc ⇒ a⁴ca³ba	[11]
7.	a⁴bc ⇒ ca³ba	[7]
8.	ba²c ⇒ a⁴c	[8]
9.	ba⁶c ⇒ cac	[9]
10.	ba²ba ⇒ c	[3]
11.	ba²bc ⇒ ca³ba	[5]

# ab:aaaaba=baaba reversed:ac/b baaba=c magic:0
aaaacac=caaaaac
aaaaaaaac=cac
aaaacaaaaac=cacac
caba=aaaac
aaaaba=c
cabc=aaaacaaaba
aaaabc=caaaba
baac=aaaac
baaaaaac=cac
baaba=c
baabc=caaaba